The Liberal Democrat insisted the better-off were benefiting disproportionately from the tax break.

The comments could increase the pressure on Chancellor George Osborne to target the rich in next month's Budget.

Reducing tax relief from 40% to 20% would save more than £7 billion and make the system fairer, according to Mr Alexander.

He told the Daily Telegraph: "If you look at the amount of money that we spend on pensions tax relief, which is very significant, the majority of that money goes to paying tax relief at the higher rate."

Lib Dem activists are expected to pass a motion calling for cuts in tax relief for higher-rate savers at the party's spring conference next month. And the Cabinet minister indicated that he was likely to vote in favour. "I'm willing to study that motion but I dare say I will," he said.

"I wrote an election manifesto at the last election which proposed going considerably further for precisely the reasons of fairness that I've set out. As a Coalition government, we've made some decisions in this area already, which go in the right direction. When it comes to people on low and middle income, I am a tax-cutter by instinct."

However, he refused to say whether the move was being discussed for next month's financial package.

Deputy Prime Minister Nick Clegg has already said he wants to move "further and faster" with increasing the tax-free allowance to £10,000 - a call that has not been endorsed by the Tories.

The coalition parties are also believed to be at odds over whether to keep the 50p top rate of tax, and introduce a "mansion tax" on high-value homes. Mr Osborne is expected to resist any calls to scrap higher-rate tax relief.